Introduction to quantum computing
This course introduces quantum computing from a mathematical perspective. No prior knowledge of quantum physics is required: the theory is built from a small set of (physics-motivated) axioms, with a focus on algorithmic principles and the underlying mathematical structures.
Core topics include the quantum circuit model, quantum gates and reversible computation, tensor products and composite systems, entanglement and measurement, and an introduction to density matrices and mixed states.
The course also covers a selection of fundamental quantum algorithms, including Grover's search algorithm, Simon's algorithm, and Shor's factoring algorithm.
Advanced topics are drawn from two areas. In quantum error correction: stabiliser codes and basic fault-tolerance principles. In quantum circuits and complexity: quantum Fourier transform, phase estimation, and structural aspects of quantum circuit complexity.
The overall goal is to prepare students for a follow-up course on quantum machine learning in the spring semester of 2027.
References:
G. Nannicini,
An Introduction to Quantum Computing, without the Physics,
SIAM Review, 62, No. 4, (2020) 936-981.
J. Buchmann,
Introduction to Quantum Algorithms,
AMS, 2024.
S. Herbert,
Quantum Computing - Foundations and Practice,
Oxford University Press, 2025.
W. Scherer,
Mathematics of Quantum Computing - An Introduction,
Springer, 2019.
A. Al-Qasimi, D. F. V. James,
Quantum Information - A First Course,
Cambridge University Press, 2025.
P. Kaye, R. Laflamme, and M. Mosca,
An Introduction to Quantum Computing,
Oxford University Press, 2006.
M. A. Nielsen and I. Chuang,
Quantum Computation and Quantum Information,
Cambridge University Press, 2002.
3 hrs / week:
Mandatory assignment: 1 project in groups of up to 3 students.
Exam: oral
Recommended background: Prior knowledge of linear algebra is helpful but not required.
To attend, please email kurusch.ebrahimi-fard @ ntnu.no and fride.straum @ ntnu.no, and register in Studentweb.
NB: We will have a meeting the week before the lectures start to give information about the course. This will be on Friday, 14. August at 10.00 in room Simastuen 656, SB2.